In the figure below, mZAHE = (6x + 7)º

43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin

Sonbull [250]

Set up
Let the dimes = d
Let the pennies = p
Let the quarters = q

Equations
You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters.

p + d + p = 43 (1)
p = d (2)
p +10d +25q = 451 (3)

Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.

Put the results of 2 into 1.
2p + q = 43 (4)
You need to modify equation 3 as well.
p + 10p + 25q = 451
11p + 25q = 451 (5)

Solve the new equations
2p + q = 43 (4)
11p + 25q = 451 (5)

Multiply 4 by 25
25(2p- + q = 43)
50p + 25q = 1075 (6) Subtract (5) from (6)
<u>11p + 25q = 451
</u>39p = 624 Divide by 39
p = 624 / 39
p = 16

Since the pennies and dimes are equal there are 16 dimes
p + d + q = 43
16 + 16 + q = 43
32 + q = 43
q = 11

Check
16 + 10*16 + 11*25 = ?
16 + 160 + 275 = ?
451 = ?

Nice problem. Thanks for posting.

3 0

4 years ago

When we test Upper H 0: muequals0 against Upper H Subscript a: mugreater than0, we get a P-value of 0.03. a. What would the

Anastasy [175]

Answer:

(a) The null hypothesis will be rejected.

(b) Type I error

(c) The null hypothesis will not be rejected. The error is type II error.

Step-by-step explanation:

The hypothesis provided is:

$H_{0}: \mu = 0\\ H_{a} : \mu > 0$

The p-value of the test obtained is 0.03

(a)

Decision rule for hypothesis testing, based on p-value, states that if the p-value is less than the significance level (α) then the null hypothesis is rejected and vice versa.

The significance level is α = 0.10

Then,

$p-value = 0.03 < \alpha = 0.10$

Thus, the null hypothesis will be rejected.

Conclusion:

The null hypothesis is rejected stating that the value of μ is more than 0.

(b)

If the decision in (a) is an error, i.e. the null hypothesis is rejected when in fact it is true, this type of error is known as type I error.

(c)

The significance level is α = 0.01

Then,

$p-value = 0.03 > \alpha = 0.01$

Thus, the null hypothesis will not be rejected.

Conclusion:

The null hypothesis was not rejected stating that the value of μ is 0.

If this decision is an error, i.e. the null hypothesis was not rejected when in fact it is false, this type of error is known as type II error.

3 0

3 years ago

A case of Mountain Dew (24 cans) cost $7.68. What is the unit price?

Westkost [7]

0.32 cents for each unit because if you divide 7.68 by 24 it is 0.32

3 0

4 years ago

Read 2 more answers

Write out the sample space for the given experiment. Use the following letters to indicate each choice: W for white, Y for yello

allochka39001 [22]

Answer:

S={WG, WE, WM, YG, YE, YM, BG, BE, BM}

Step-by-step explanation:

There are three possible color choices for the game room (White, Yellow or Blue), and three possible choices for the entertainment center (Gray, Ebony or Maple). This means that there are 9 possible outcomes, therefore, the sample space for the experiment is:

S={WG, WE, WM, YG, YE, YM, BG, BE, BM}

4 0

3 years ago

Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches

Mrac [35]

The answer is B.) 3

I hope this helped!

8 0

3 years ago

Read 2 more answers